Author: Christopher A. Kennedy
Publisher:
ISBN:
Category : Finite differences
Languages : en
Pages : 66

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Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781730740299
Category : Science
Languages : en
Pages : 64

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Book Description
An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist. Kennedy, Christopher A. and Carpenter, Mark H. Langley Research Center...

Author: Christopher A. Kennedy
Publisher:
ISBN:
Category :
Languages : en
Pages : 538

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Author: Ronald Frederick Burr
Publisher:
ISBN:
Category :
Languages : en
Pages : 333

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Book Description
Numerical modeling and numerical simulation of compressible reacting turbulent shear layers are considered in the current research effort. In the numerical modeling portion of this work, improved turbulent transport models for compressible shear layers are presented and validated with detailed experimental data. In the second major emphasis of the present research effort, numerical simulations of temporally evolving compressible and reacting shear layers are performed. The results are examined in terms of the steady-state shear layer modeling techniques.

Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781719402545
Category :
Languages : en
Pages : 30

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The objective of this work is to compare a high-order solver with a low-order solver for performing Large-Eddy Simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the highorder method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing. Mankbadi, Mina R. and Georgiadis, Nicholas J. and DeBonis, James R. Glenn Research Center COMPUTATIONAL FLUID DYNAMICS; LARGE EDDY SIMULATION; TURBULENT MIXING; SHEAR LAYERS; COMPRESSIBLE BOUNDARY LAYER; BOUNDARY CONDITIONS; MATHEMATICAL MODELS; COMPUTATIONAL GRIDS

Author: Alain Dervieux
Publisher: Springer Science & Business Media
ISBN: 3322898598
Category : Technology & Engineering
Languages : en
Pages : 580

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Book Description
This volume contains contributions to the BRITE-EURAM 3rd Framework Programme ETMA and extended articles of the TMA-Workshop. It focusses on turbulence modelling techniques suitable to use in typical flow configurations, with emphasis on compressibility effects and inherent unsteadiness. These methodologies are applied to the Navier-Stokes equations, involving various turbulence modelling levels from algebraic to RSM. Basic turbulent flows in aeronautics are considered; mixing layers, wall-flows (flat-plate, backward-facing step, ramp, bump), and more complex configurations (bump, aerofoil). A critical assessment of the turbulence modelling performances is offered, based on previous results and on the experimental data-base of this research programme. The ETMA results figure in the data-base constituted by all partners and organized by INRIA

Author: Rainer Friedrich
Publisher: Springer Science & Business Media
ISBN: 1402023138
Category : Science
Languages : en
Pages : 652

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Book Description
The fifth ERCOFfAC workshop 'Direct and Large-Eddy Simulation-5' (DLES-5) was held at the Munich University of Technology, August 27-29, 2003. It is part of a series of workshops that originated at the University of Surrey in 1994 with the intention to provide a forum for presentation and dis cussion of recent developments in the field of direct and large-eddy simula tion. Over the years the DLES-series has grown into a major international venue focussed on all aspects of DNS and LES, but also on hybrid methods like RANSILES coupling and detached-eddy simulation designed to provide reliable answers to technical flow problems at reasonable computational cost. DLES-5 was attended by 111 delegates from 15 countries. Its three-day pro gramme covered ten invited lectures and 63 original contributions partially pre sented in parallel sessions. The workshop was financially supported by the fol lowing companies, institutions and organizations: ANSYS Germany GmbH, AUDI AG, BMW Group, ERCOFfAC, FORTVER (Bavarian Research Asso ciation on Combustion), JM BURGERS CENTRE for Fluid Dynamics. Their help is gratefully acknowledged. The present Proceedings contain the written versions of nine invited lectures and fifty-nine selected and reviewed contributions which are organized in four parts: 1 Issues in LES modelling and numerics 2 Laminar-turbulent transition 3 Turbulent flows involving complex physical phenomena 4 Turbulent flows in complex geometries and in technical applications.

Author: Maria Vittoria Salvetti
Publisher: Springer Science & Business Media
ISBN: 9400702310
Category : Science
Languages : en
Pages : 442

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Book Description
The second Workshop on "Quality and Reliability of Large-Eddy Simulations", QLES2009, was held at the University of Pisa from September 9 to September 11, 2009. Its predecessor, QLES2007, was organized in 2007 in Leuven (Belgium). The focus of QLES2009 was on issues related to predicting, assessing and assuring the quality of LES. The main goal of QLES2009 was to enhance the knowledge on error sources and on their interaction in LES and to devise criteria for the prediction and optimization of simulation quality, by bringing together mathematicians, physicists and engineers and providing a platform specifically addressing these aspects for LES. Contributions were made by leading experts in the field. The present book contains the written contributions to QLES2009 and is divided into three parts, which reflect the main topics addressed at the workshop: (i) SGS modeling and discretization errors; (ii) Assessment and reduction of computational errors; (iii) Mathematical analysis and foundation for SGS modeling.

Author: Viktor Linders
Publisher: Linköping University Electronic Press
ISBN: 9176854272
Category :
Languages : en
Pages : 44

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Book Description
In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to weakly impose boundary conditions. The SBP-SAT framework combines high order of accuracy with a systematic construction of provably stable boundary procedures, which renders it suitable for a wide range of problems. The first part of the thesis treats wave propagation problems discretised using SBP operators on coarse grids. Unless special care is taken, inaccurate approximations of the underlying dispersion relation materialises in the form of an incorrect propagation speed. We present a procedure for constructing SBP operators with minimal dispersion error. Experiments indicate that they outperform higher order non-optimal SBP operators for flow problems involving high frequencies and long simulation times. In the second part of the thesis, the formal order of accuracy of SBP operators near boundaries is analysed. We prove that the order in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. This generalises the classical theory posed on uniform and conforming grids. We further show that for a common class of SBP operators, the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid. In the final contribution if the thesis, we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability analyses are performed for continuous and discrete problems. A general condition is obtained that is necessary and sufficient for the transmission problem to satisfy an energy estimate. The theory provides insights into the coupling of fluid flow models, multi-block formulations, numerical filters, interpolation and multi-grid implementations.

Author: Carlos Arturo Gomez Elizondo
Publisher:
ISBN:
Category :
Languages : en
Pages : 180

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Book Description
Compressibility profoundly affects many aspects of turbulence in high-speed flows - most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. Many of the features observed in compressible flows are due to the changing nature of pressure. Whereas for incompressible flows pressure merely serves to enforce incompressibility, in compressible flows pressure becomes a thermodynamic variable that introduces a strong coupling between energy, state, and momentum equations. Closure models that attempt to address compressibility effects must begin their development from sound first-principles related to the changing nature of pressure as a flow goes from incompressible to compressible regime. In this thesis, a unified framework is developed for modeling pressure-related compressibility effects by characterizing the role and action of pressure at different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for the pressure-strain correlation, pressure-dilatation and dissipation evolution equation. The pressure-strain correlation closure coefficients are established using fixed point analysis by requiring consistency between model and direct numerical simulation asymptotic behavior in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing-layers and boundary layers in a differential Reynolds stress modeling solver. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing relative Mach number are all well captured. High-speed boundary layer results are also adequately replicated even without the use of advanced thermal-flux models or low Reynolds number corrections. To reduce the computational burden required for differential Reynolds stress calculations, the present compressible pressure-strain correlation model is incorporated into the algebraic modeling framework. The resulting closure is fully explicit, physically realizable, and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. The new algebraic model is validated with direct numerical simulations of homogeneous shear flow and experimental data of high-speed mixing-layers. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of direct numerical simulations quite well. Calculations of plane supersonic mixing-layers are performed and comparison with experimental data shows good agreement. Therefore the algebraic model may serve as a surrogate for the more computationally expensive differential Reynolds stress model for flows that permit the weak-equilibrium simplification. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148160